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FloatingPoint Arithmetic
, 1992
"... GEM computer users, for better or for worse, will interact with the IEEE Standard for Binary FloatingPoint Arithmetic (IEEE 754). All of today's popular RISC/UNIX architectures support the IEEE 754 standardboth in data format and exception handling. However, details of the IEEE 7 54 exception ..."
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GEM computer users, for better or for worse, will interact with the IEEE Standard for Binary FloatingPoint Arithmetic (IEEE 754). All of today's popular RISC/UNIX architectures support the IEEE 754 standardboth in data format and exception handling. However, details of the IEEE 7 54
New directions in floatingpoint arithmetic
"... Abstract. This article briefly describes the history of floatingpoint arithmetic, the development and features of IEEE standards for such arithmetic, desirable features of new implementations of floatingpoint hardware, and discusses workinprogress aimed at making decimal floatingpoint arithmetic ..."
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Abstract. This article briefly describes the history of floatingpoint arithmetic, the development and features of IEEE standards for such arithmetic, desirable features of new implementations of floatingpoint hardware, and discusses workinprogress aimed at making decimal floatingpoint
Adaptive Precision FloatingPoint Arithmetic and Fast Robust Geometric Predicates
 Discrete & Computational Geometry
, 1996
"... Exact computer arithmetic has a variety of uses including, but not limited to, the robust implementation of geometric algorithms. This report has three purposes. The first is to offer fast softwarelevel algorithms for exact addition and multiplication of arbitrary precision floatingpoint values. T ..."
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Cited by 172 (5 self)
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on computers whose floatingpoint arithmetic uses radix two and exact rounding, including machines complying with the IEEE 754 standard. The inputs to the predicates may be arbitrary single or double precision floatingpoint numbers. C code is publicly available for the 2D and 3D orientation and incircle tests
FloatingPoint LLL Revisited
, 2005
"... The LenstraLenstraLovász lattice basis reduction algorithm (LLL or L³) is a very popular tool in publickey cryptanalysis and in many other fields. Given an integer ddimensional lattice basis with vectors of norm less than B in an ndimensional space, L³ outputs a socalled L³reduced basis in po ..."
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Cited by 53 (7 self)
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in polynomial time O(d 5 n log³ B), using arithmetic operations on integers of bitlength O(d log B). This worstcase complexity is problematic for lattices arising in cryptanalysis where d or/and log B are often large. As a result, the original L³ is almost never used in practice. Instead, one applies floatingpoint
An efficient algorithm for exploiting multiple arithmetic units
 IBM JOURNAL OF RESEARCH AND DEVELOPMENT
, 1967
"... This paper describes the methods employed in the floatingpoint area of the System/360 Model 91 to exploit the existence of multiple execution units. Basic to these techniques is a simple common data busing and register tagging scheme which permits simultaneous execution of independent instructions ..."
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Cited by 389 (1 self)
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optimizes the program execution on a local basis. The application of these techniques is not limited to floatingpoint arithmetic or System/360 architecture. It may be used in almost any computer having multiple execution units and one or more 'accumulators.' Both of the execution units, as well
Highprecision floatingpoint arithmetic in scientific computation
 Computing in Science and Engineering, May–June
, 2005
"... At the present time, IEEE 64bit floatingpoint arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing applications, a higher level of numeric precision is required: some of these applications require roughly twice ..."
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Cited by 19 (1 self)
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At the present time, IEEE 64bit floatingpoint arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing applications, a higher level of numeric precision is required: some of these applications require roughly twice
The pitfalls of verifying floatingpoint computations
 ACM Transactions on programming languages and systems
"... Current critical systems often use a lot of floatingpoint computations, and thus the testing or static analysis of programs containing floatingpoint operators has become a priority. However, correctly defining the semantics of common implementations of floatingpoint is tricky, because semantics ma ..."
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Cited by 56 (3 self)
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Current critical systems often use a lot of floatingpoint computations, and thus the testing or static analysis of programs containing floatingpoint operators has become a priority. However, correctly defining the semantics of common implementations of floatingpoint is tricky, because semantics
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